Signalised lead ins are helpful to solve flow issues caused by an imbalance in traffic direction at certain times of day. When you get too much traffic building up that can’t enter the roundabout due to no gaps you activate the red light before the entrance dominating traffic flow to give a period where the other directions can move through. The actual roundabout works as per normal and you don’t have to deal with lights during non-peak periods.

Lights on a roundabout make it not really a roundabout but an unholy mishmash of intersection design. I’ve got one near me and the only thing going for it was that converting a roundabout was significantly cheaper than the flyover intersection it really should be made into.

One of the work trucks used to have one that said “Go straight through the roundabout”. It was pretty tempting sometimes to take it at its word…